Department of Mathematics
We consider an inverse acoustic scattering problem in simultaneously recovering an embedded obstacle and its surrounding inhomogeneous medium from formally determined far-field data. It is shown that knowledge of the scattering amplitude with a fixed incident direction and all observation angles along with frequencies from an open interval can be used to uniquely identify the embedded obstacle, sound-soft or sound-hard, irrepective of the surrounding medium. Furthermore, if the surrounding inhomogeneous medium is from an admissible class (still general), then the medium can be recovered as well. Our argument is based on deriving certain integral identities involving the unknowns and then inverting them by certain harmonic analysis techniques. Finally, based on our theoretical study, a fast and robust sampling method is proposed to reconstruct the shape and location of the buried targets and the support of the surrounding inhomogeneities.
inverse acoustic scattering, obstacle, medium, unique identifiability, simultaneous, formally determined
Source Publication Title
This is an author-created, un-copyedited version of an article accepted for publication published in Inverse Problems. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at http://dx.doi.org/10.1088/1361-6420/aa6770.
The work of H Liu was supported by the FRG fund from Hong Kong Baptist University, the Hong Kong RGC grants (projects 12302415 and 405513) and the NNSF of China (No. 11371115). The work of X Liu was supported by the NNSF of China under grants 11571355, 61379093 and 91430102.
Link to Publisher's Edition
Liu, H., & Liu, X. (2017). Recovery of an embedded obstacle and its surrounding medium from formally determined scattering data. Inverse Problems, 33 (6), 065001. https://doi.org/10.1088/1361-6420/aa6770